The influence of strain rate on the interfacial fracture toughness between PVB and laminated glass

Transcription

1 J. Phys. IV France 134 (26) C EDP Sciences, Les Ulis DOI: 1.151/jp4: The influence of strain rate on the interfacial fracture toughness between PVB and laminated glass R. Iwasaki 1 and C. Sato 2 1 Graduate School of Tokyo Institute of Technology, 4259, Nagatsuta-cho, Midori-ku, Yokohama, Japan 2 Precision & Intelligence laboratory, Tokyo Institute of Technology, Japan Abstract. This paper presents the experimental results of high speed tests using laminated safety glass to determine the interfacial fracture toughness between PVB (polyvinyl butyral) sheets and glass plates. Low-speed tensile test of PVB was carried out firstly. PVB shows a non-linear visco-elastic property. The property was described using a non-linear visco-elastic model. The visco-elastic parameters were calculated to compare the experimentally obtained stress-strain curves and the results of simulation. A simple fracturemechanical model for PVB laminated glass was conducted to determine the energy release rate G. The fracture toughness G c of the PVB laminated glass specimens were calculated from both the results of lowspeed tensile tests and the equation for the energy release rate. The strain-stress curves of PVB under high strain rates are totally different from those of the low speed tests. The phenomenon can be explained from the phase transition due to the difference of strain rates because the mechanical properties of PVB changes from visco-elastic to glassy behavior. The fracture toughness of PVB laminated glass was calculated from the experimental results of high speed tests. Fracture energy was defined and also compared to the fracture toughness. 1. INTRODUCTION PVB (Poly vinyl butyral) laminated glass is used for the front glass of cars to absorb the impact in case of the accident. The PVB laminated glass has also another advantage to keep the clearness of the view for the driver even in the case of collisions with the small pebbles. Totally reinforced glass has not such a capability because it breaks into small pieces in the same situation. In recent years, the use of the PVB laminated glass has been expanding compared to the other materials. For instance, cars with a glass roof have been available. The situation causes new technical demands for it to bear the impact of heavier bodies at comparably low velocity. Many experiments have been conduced to investigate the fracture toughness of PVB laminated glass [1]. The influence of the surface treatment on the adhesion between PVB and glass has also been investigated [2]. However, they are practical experiments and they cannot be applied to the simulations directly based on fracture mechanics and/or stress-strain analysis. One of the difficulties is that the formulation of PVB-glass interfacial strength under high strain rates has not been established yet. In this research, the mechanical behavior of PVB and PVB laminated glass subjected to a tensile load of various rates are investigated experimentally. The fracture toughness and fracture energy of the PVB laminated glass are also calculated. 2. FRACTURE TOUGHNESS AND FRACTURE ENERGY To calculate the fracture toughness and the fracture energy of PVB laminated glass, a configuration shown in fig.1 is considered. From material mechanics, the energy release rate G of the model is derived as follows: G = F 2 { 1 1 }. (1) 2w 2 E p t p E G t G Article published by EDP Sciences and available at or

2 1154 JOURNAL DE PHYSIQUE IV Figure 1. Configuration and dimensions of PVB laminated glass specimen. Where F is the applied force, w is the width of the specimen, E P and E G refer to the Young s modulus of PVB and glass and t P and t G are termed the thickness of PVB and glass, respectively. The fracture toughness G c of the PVB/Glass interface is calculated from equation 1 based on the critical load obtained from the tensile test of the PVB laminated glass. To take the energy dissipated in the PVB non-linear deformation into consideration from experimental results, the integrals of the force-displacement curve until crack propagation are used to analyze the strength of the adhesively bonded joints. Here, the integral of the applied force is defined as fracture energy U c. Thus, the fracture energies is U c = r c Fdr A (2) and where A is the pre-cracked area of the PVB-glass specimen. The formula represents the whole energy consumed, the crack propagation divided by the pre-crack area of the PVB-glass specimen. The fracture strength of the PVB laminated glass is investigated using two parameters G c and U c. 3. SPECIMENS 3.1 PVB specimen JIS 2 type specimens, shown in fig.2 were made from PVB sheets (thickness:.76mm) using a punch. 3.2 PVB laminated glass specimens Two or four sheets of slide glass (thickness: 1.mm) and a PVB sheet was used to prepare a PVB laminated glass specimen. A configuration of the specimen contained two slides is shown in fig.1. Another configuration having four glasses was also used. Pre-cracks were made using the release solvent. The conditions of the curing was 13 C, 1hour using the vacuum bag.

3 EURODYMAT Unit: mm Figure 2. Configuration and dimensions of PVB specimen [3]. 4. EXPERIMENTAL PROCEDURE 4.1 Low speed tensile test Low speed tensile tests were carried out for PVB specimens using a tensile test apparatus (LSC-5/3, Tokyo Testing Machine Inc.). An optical extensometer (SS-22D, Tokyo Testing Machine Inc.) was utilized to measure the large deformation (strain) of PVB. Low speed tensile tests of PVB laminated glass were carried out using another tensile test apparatus (AUTOGRAPH AGS-5A, Shimadzu Corporation) and the crack propagation was observed by a CCD camera. 4.2 High speed tensile test High speed tensile tests were conducted for both PVB specimens and PVB laminated glass specimens using a high speed tensile test machine shown in fig.3. A specimen was fixed by two crossheads. The projectile hits the bottom of the crosshead to provide for the specimen with the tensile load in high speed. Maximum tensile speed is 1m/s. The laser displacement sensor (LB3, Keyence Corporation) is used to measure the displacement of the crosshead and the quartz load cell (931B, Kistler Instrument AG) is used to measure the load. A high speed camera (FASTCAM-APX RS 25K/25KC, Photoron ltd.) is also used to film the deformation of the PVB specimens and the crack propagation of the PVB laminated glass specimens. 5. RESULTS AND DISCUSSION 5.1 PVB tensile test Stress-strain curves obtained from the low speed tensile test of PVB is shown in fig.4. It is considered that the steepness of the stress-strain curves depends on the tensile speed. The inclination becomes steep with respect to the increase of the tensile speed. The property can be explained generally by a viscoelastic model [4]. To apply for the PVB specimens, the model is modified to have a dashpot, linear spring and a non-linear spring as follows: f (ε) σ = E 2 ε + E 1 ε E 2 ε η (σ E 1f (ε)). (3) where σ is a stress, ε is a strain, f is a non-linear function and E 1 and E 2 are the Young s modulus of linear and non-linear springs, respectively.

4 1156 JOURNAL DE PHYSIQUE IV PVB specimen Crack of PVB laminated glass specimen Figure 3. High speed tensile test machine and captured images of the specimens. Typical strain-stress curves of PVB obtained from the low-speed and the high speed tensile tests are shown in fig.5. It seems that PVB behaves as an elasto-plastic material under the high rate of tensile load. It is also shown that the tangential Young s modulus at the beginning of the tensile test increases drastically compared with that of the low speed tensile test. The stress-strain curves of low speed test are similar to that of amorphous polymers above glass the transition temperature: T g [5] and the stress-strain curves of high speed test resemble to the curves of the amorphous polymer below T g [5]. This tendency, the transition through T g,, corresponds to the transition occurring in the shift of the strain rate, and has good agreement with the Eyring s theory [6]. 5.2 Tensile test of PVB laminated glass Critical loads of crack initiation under various tensile speeds are shown in fig.6. The critical loads increase with respect to the tensile speed and they show approximately the same results with various pre-crack lengths. The elastic modulus E P is derived from the tensile tests of PVB in order to calculate the fracture toughness G C. Each elastic modulus corresponds to the tangential elastic modulus at the beginning point of crack propagation. The fracture toughness of the PVB/glass interface for varying pre-crack lengths is shown in fig.7. The fracture toughness becomes smaller under high speed tensile loads. The reason for this phenomenon is considered that the tangential elastic modulus of PVB is much higher under the high tensile speed, especially in the elastic area, than the modulus under the low tensile loads. The fracture energy of the PVB/glass interface is shown in fig.8. The fracture energy is larger than the fracture toughness in all

5 EURODYMAT Stress (MPa) (1/s).33 (1/s).67 (1/s).13 (1/s).2 (1/s) Strain (%) Figure 4. Stress-strain curve of PVB at low strain rates rate. Stress (MPa) (1/s).33 (1/s) Strain (%) Figure 5. Stress-strain curve of PVB at high strain. Load (N) x1-4 m/s 5.x1-3 m/s 2.96 m/s Pre-crack length (mm) Fracture toughness (J/m 2 ) x1-4 m/s 5.x1-3 m/s 2.96 m/s Pre-crack length Figure 6. Critical loads of crack initiation glass. Figure 7. Fracture toughness of PVB laminated. Fracture energy (J/m 2 ) x1-4 m/s 5.x1-3 m/s 2.96 m/s Figure 8. Fracture energy of PVB laminated glass Pre-crack length (mm) the experimental results. This result seems quite natural because the fracture energy can consist of the fracture energy and the energy consumed by the deformation of the free (not adhered to the glass) part of the PVB, theoretically. From the observation using the CCD camera, the free part of the PVB in the laminated glass deforms 7-1% and the stress reaches 2.5 MPa until the crack propagation occurs in the low speed tensile test.

6 1158 JOURNAL DE PHYSIQUE IV Contrary, to the observation using the high speed camera in the high tensile test, the PVB deform only 1-15% and the stress reaches 1 MPa, which is in the elastic area under a high strain rate, until the crack propagation. The energies consumed by the deformation of the free PVB are in the same order. Consequently, fracture energies of the high speed and the low speed test have approximately the same values. 6. CONCLUSION The mechanical behavior of PVB laminated glasses are investigated experimentally and the fracture toughness and the fracture energy are calculated for PVB laminated glass. The results suggest that the mechanism of PVB deformation and crack propagation in high tensile speed is different from that in low tensile speed but the fracture energy and fracture toughness under the low tensile rates are similar to that under the high tensile rate. Acknowledgments The authors are grateful to K. Aizawa (Photoron Ltd.) for the experiment using the high-speed imaging system. References [1] R.A.Behr, M.J.Karson and J.E.Minor, Structural Safety 11 (1991) [2] A.V.Gorokhovsky and K.N.Matazov, J. Adh. Sci. Tech. (2) [3] JIS K [4] Y.M.Haddad, Viscoelasticity of Engineering Materials (Chapman & Hall, London, 1995) pp [5] Y.J.Juang, L.J.Lee and K.W.Koelling, Poly. Eng. Sci. (21) [6] H.Eyring, J. Chem. Phys. (1936)